Stephen -- Have you ever been South? Many Brits are uncomfortable about how curious and personal Americans can be with questions that we, Americans just consider being friendly. Well, they're usually talking about the North which we consider a pretty standoffish place. Even attending a professional games in the US (you mentioned you went with your Dad, IIRC) is nothing like going to a college game in the South.
What I'm getting at is that you should expect culture shock despite having been to the US before.
If you come to Knoxville wearing Big Orange expect to be overwhelmed with kindness. People will overwhelm you with offers of food, drink, etc. and will want to get to know you. That's not strange but rather normal for us. Even if you go to Tuscaloosa, you can expect the same treatment, especially prior to the game. And if you tell a group of tailgaters from either team that you've come across the pond to watch the greatest football rivalry known to man, you can expect to get treated like a King whether you're sporting orange in Knoxville or Tuscaloosa, especially pre-game. Southerners pride ourselves on our hospitality.
As others have said, Gainesville isn't worth the trip. They're a different breed altogether.